By RICHARD W. STEVENSON and JANET ELDER

Published: October 5, 2004

Senator John Kerry came out of the first presidential debate having reassured many Americans of his ability to handle an international crisis or a terrorist attack and with a generally more favorable image, but he failed to shake the perception that he panders to voters in search of support, according to the latest New York Times/CBS News poll.

The poll also found significant doubts about President Bush's policies toward Iraq, with a majority of the public saying that the United States invaded too soon and that the administration did a poor job thinking through the consequences of the war. But Mr. Bush maintained an advantage on personal characteristics like strong leadership and likability, as well as in the enthusiasm of his supporters.

Four weeks from Election Day, the presidential race is again a dead heat, with Mr. Bush having given up the gains he enjoyed for the last month after the Republican convention in New York, the poll found. In both a head-to-head matchup and a three-way race including Ralph Nader, the Republican and Democratic tickets each won the support of 47 percent of registered voters surveyed in the poll.

Last month, Mr. Bush led Mr. Kerry by 50-42 in a two-way race and 50-41 in a three-way race.

The results, which parallel those of several other national polls in the past few days, are likely to intensify interest in tonight's debate in Cleveland between the vice-presidential candidates, Senator John Edwards of North Carolina and Vice President Dick Cheney, as well as the two additional presidential debates, on Friday and Oct. 13.

Aides to both campaigns said yesterday that the running mates' debate, which begins at 9 p.m. Eastern time, was unlikely to have a major impact on the vote in November. That did not stop them, though, from trying once again to set high expectations for the other side, as each campaign pointed to the debating strengths of its opponents.

Some of the drop in Mr. Bush's numbers appeared to reflect the traditional cycle in which a candidate's standing surges after his nominating convention and then declines somewhat. Both the Bush and Kerry campaigns have said for months that they expect the race to be tight at the very end.

But Mr. Kerry also scored notable gains in several areas that could be vital in a campaign being largely fought over the war in Iraq and the threat of terrorism.

Forty-one percent of registered voters said they had confidence in Mr. Kerry's ability to deal wisely with an international crisis, up from 32 percent before the debate. Thirty-nine percent said they had a lot of confidence that Mr. Kerry would make the right decisions when it came to protecting against a terrorist attack, up 13 percentage points.

On both scores, however, Mr. Kerry still trailed Mr. Bush. Fifty-one percent of voters said they had confidence in Mr. Bush's ability to deal with an international crisis, unchanged from before the debate, and 52 percent said they had a lot of confidence in his ability to protect against a terrorist attack, up slightly from 50 percent last month.

Mr. Bush's strategy of portraying Mr. Kerry as an unprincipled flip-flopper appears to have stuck in the national consciousness. Sixty percent of registered voters said Mr. Kerry told people what they wanted to hear rather than what he really believed, about the same level as throughout the spring and summer. The corresponding figure for Mr. Bush was 38 percent.

It is unclear whether the race for the White House has merely reverted to a steady state in which neither candidate can establish a clear lead, whether Mr. Bush can regain the advantage with a strong performance in the next debates or whether Thursday was a turning point at which Mr. Kerry seized the initiative.

There is also considerable uncertainty over whether national polling numbers reflect the state of play in the 18 or so swing states where the election will be decided and where the relative success of get-out-the-vote efforts by both sides could prove to be the difference. In recent weeks there has been a surge of new voter registrations in many states as the two campaigns and their allies seek to ensure that every possible supporter goes to the polls on Nov. 2.

The Kerry campaign said the poll showed that the race was moving in its direction. The nationwide telephone poll of 979 adults included 851 registered voters. The margin of sampling error for the entire sample, and for registered voters, is plus or minus three percentage points.

''The public took a measure of John Kerry standing next to the president, and came to the conclusion that he had the strength, judgment and experience to be the commander in chief,'' said Joe Lockhart, a senior strategist for Mr. Kerry.

Mr. Bush's team said he remained ahead in the ways that would count most on Election Day.

''We always said this race would be close,'' said Matthew Dowd, Mr. Bush's chief campaign strategist. ''When style fades quickly, leadership and policies remain, and that is where the president has the advantage.''

Over all, Mr. Kerry appears to have come off well in the debate, which respondents to the poll said, 60 percent to 23 percent, that he won.